Finding the differential of the function

We just finished linear approximations and differentials in our course and was hoping I could get some feedback on this question of mine. The following question I have is asking to find the differential of the function:

y= cos(pi)x

We know from the formula

dy = f'(x)*dx

However, we are supposed to use our product rule here to determine the derivative of cos(pi)x.

I came up with -(pi)sin(pi)x but I'm not sure how to solve from that using the rule. The rest is fairly straight forward because it's just putting it back into the formula. Thanks guys for any help.